Question

39. Sum to n terms of the series sino sin20 + sin20 sin30 + sin30 sin4e + is equal to n n () (1) cose 1 sin ne ..cos(n +2) 2 sino (2) sine - sin 1 sin ne 2 2. 2 n 3) (3) cose coso - cos (n +2) (4) sino + sinne 2
​

Answer 1

Answer:

Question

Bookmark

If x=cosθ+isinθ the value of x

n

+

x

n

1

is

Medium

Solution

verified

Verified by Toppr

Correct option is

A

2cosnθ

x=cosθ+isinθ

Applying Euler's form

x=cosθ+isinθ=e

iθ

.

Hence

x

n

=e

inθ

.

Similarly

x

1

=

x

ˉ

=cosθ−isinθ=e

−iθ

Hence

x

n

1

=e

−inθ

.

Hence

x

n

+

x

n

1

=e

inθ

+e

−inθ

=cosnθ+isinnθ+cosnθ−isinnθ

=2cosnθ.